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[tex]b = 2 - \dfrac 1a\\\\\implies ab = 2a -1\\\\\implies 2a -ab = 1\\\\\implies a(2-b) =1\\\\\implies a = \dfrac 1{2-b}[/tex]

Answer: The image listed below. It's the only valid answer that best shows the numbers of toys Roldlfo has in his toy box, y, and the number of months that have passed, x.

Answer 1/614

Step-by-step explanation:

Answer:

Step-by-step explanation:

as (c + 9)(c - 9) = c² - 81

and (c - 9)(c + 6) = c² - 3c - 54

    8(c + 6)        =         8c + 48        

(c² - 81)(c + 6)       (c - 9)(c + 9)(c + 6)

            10c(c + 9)     =     10c² + 90c        

(c² - 3c - 54)(c + 9)       (c - 9)(c + 9)(c + 6)

The equivalent rational expressions with denominator (c- 9) (c+9)(c + 6) are;

1.  8 / (c² - 81) = 8 / (c + 9) (c - 9)

2. 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expressions are,

1. 8 / (c² - 81)

2. 10c / (c² - 3c - 54)

Now,

Solve the expressions for the denominator (c- 9) (c+9)(c + 6) as;

1. 8 / (c² - 81) = 8 / (c² - 9²)

                   = 8 / (c + 9) (c - 9)

Thus, 8 / (c² - 81) = 8 / (c + 9) (c - 9)

2. 10c / (c² - 3c - 54) = 10c / (c² - (9- 6)c - 54)

                               = 10c / (c² - 9c + 6c - 54)

                               = 10c / [c(c-9) + 6(c - 9)]

                               = 10c / (c + 6) (c - 9)

Thus, 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)

Therefore, The equivalent rational expressions with denominator (c- 9) (c+9)(c + 6) are;

1.  8 / (c² - 81) = 8 / (c + 9) (c - 9)

2. 10c / (c² - 3c - 54) = 10c / (c + 6) (c - 9)

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4

the other really do not make sense

Answer:

2

Step-by-step explanation:

Answer:

1a:  [tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]

1b: See below

1c:  [tex]2\frac{3}{4}[/tex] inches between the beetle and ant

Step-by-step explanation:

1a. To build the equation, we need to see that the beetle started at 3/4th inches below ground level, then "climbed" (which is poor English, it should be descended) a certain distance, and then it ended up at 2 1/2 inches below ground. The distance "climbed" can be represented as 1/3X, where "X" is the ant's current distance. We would do 1/3rd times "X" to figure out how much the beetle climbed down.

So that means, if we added together the starting position of 3/4, plus the distance the beetle descended (1/3X), that would get us TO 2 1/2 inches below ground (the beetle's new current position). So therefore our equation is:

[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]

1b. Solve the equation written above from 1a.

[tex]\frac{3}{4}[/tex] + [tex]\frac{1}{3}x[/tex] = [tex]2\frac{1}{2}[/tex]

-3/4     -3/4   [subtract 3/4 to start the process of getting x by itself]

[tex]\frac{1}{3}x[/tex] = 1[tex]\frac{3}{4}[/tex]

*3/1   *3/1 [Multiply Reciprocal to get X by itself]

x= [tex]5\frac{1}{4}[/tex]

1c. So we take the position of the ant figured out on 1b (5 1/4 inches), and the new current position of the beetle (2 1/2 inches), and subtract them

5 1/4 - 2 1/2 =  [tex]2\frac{3}{4}[/tex]

[tex]\begin{array}{ccll} \stackrel{cm}{map}&\stackrel{mi}{actual}\\ \cline{1-2} 2&100\\ 5.4&x \end{array}\implies \cfrac{2}{5.2}=\cfrac{100}{x}\implies 2x = 520\implies x = \cfrac{520}{2}\implies x = 260[/tex]

Answer:

Step-by-step explanation:

x = orange ball count

y = green ball count

y = 3x + 7

x + (3x + 7) = 103

4x = 96

x = 24 orange balls

y = 103 - 24 = 79 green balls

or

y = 3(24) + 7 = 79

Answer:

52 green, 15 orange!

Step-by-step explanation:

take reference from the following image:

38

To get the number of games C won,you multiply the ratio of B:C,4:3 to ratio of known 8:x to get 6 as the games C won.For A,you multiply the ratio of A:B,3:1 to value of known y:8 to get 24 as the games A won.Add 8+6+24 to get total number of games won.

Answer:

15% of 40 is 6

9514 1404 393

Answer:

  $6

Step-by-step explanation:

15% is the ratio of the price increase to the original price.

As a fraction 15% = 15/100 (fifteen hundredths).

As a decimal, 15% = 0.15 (fifteen hundredths).

__

The statement about the price increase is telling you ...

  (increase)/(original) = 0.15

Multiplying by the original price, we get ...

  (increase) = 0.15×(original) = 0.15 × $40 = $6.00

The price of the shirt went up $6.00.

Answer:

x = -5

Step-by-step explanation:

If g(x)= 3x - 12, and g(x)= -27 then -27 = 3x -12

Solve for x

     -27 = 3x -12, add 12 to both sides

-27+12 = 3x, add -27+12

     -15 = 3x, divide both sides by 3

      -5 = x

Answer:-93

Step-by-step explanation:

g(x)=3x-12

g(x)=3(-27)-12   -  Substitute

g(x)=-81-12        -  Multipy

g(x)= -93             - Add

Answer:

Step-by-step explanation:

$760(1.023) = $777.48

Answer:

Pythagorean Theorem. The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs of the right triangle. This same relationship is often used in the construction industry and is referred to as the 3-4-5 Rule.

Answer:

Step-by-step explanation:

x + x + (2x + 50) = 180

4x = 130

x = 32.5°

Answer:

draw a rectangle

Step-by-step explanation:

a rectangle has 2 long sides and 2 short ones it has 2 sets of simailer and has 2 perpundicular

Answer:

6 Ways

Step-by-step explanation:

Given: 3 students, Madeline, Austin, and Aubree

To Find: How many different ways can they stand in line?

Solution: 3 students, can line up in 3 so 6 ways.

Step-by-step explanation:

No, it is not possible for a regular polygon to have 240° as the measure of each of

its interior angles.

according to the formula:

A = 180 - (360 /n)

where A is the interior angle

therefore, the A could be less than 180°

I wrote this on a document in my previous years in school.

Answer:

19

Step-by-step explanation:

they give you xz, and they want half, so just divide 38 by 2

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{(-4)}}}\implies \cfrac{-1}{-2+4}\implies \cfrac{-1}{2}\implies -\cfrac{1}{2}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{-\cfrac{1}{2}}[x-\stackrel{x_1}{(-4)}] \\\\\\ y-6=-\cfrac{1}{2}(x+4)\implies y-6=-\cfrac{1}{2}x-2\implies \underset{\textit{slope-intercept form}}{y=-\cfrac{1}{2}x+4}[/tex]

Answer:

False

Step-by-step explanation:

The sides are not equal.

Answer:

Step-by-step explanation:

A function f(x) has an inverse, or is one-to-one, if and only if the graph y = f(x) passes the horizontal line test. A graph represents a one-to-one function if and only if it passes both the vertical and the horizontal line tests.

Answer:

The slope is:

[tex] \binom{1}{2} [/tex]

In slope-intercept form the equation is:

[tex]y = \binom{1}{2} x - 3[/tex]

Answer:

what we have to do here hmm mm mm .......

Answer: the value of y is 1

Step-by-step explanation: 6=2 x 1+2

Answer:

y = 2x + 2

Step-by-step explanation:

for each rise of 4 in y

there is a run of 2 in x

m = rise/run

m = 4/2

m = 2

when x = 0, y = 2

therefor the y-intercept, b = 2

y = mx + b

y = 2x + 2

Answer:

Hello!

Judging by the link you provided I have come up with the correct solution:

x= 61°

y= 29°

Step-by-step explanation:

I will link my work below:

The first step to finding the two solutions it to first identify one of them.

I chose to identify x first.

To identify the value of x in this problem you have to notice that the x value corresponds with the value "29°" to form a perfect right angle, being 90°.

Thus you can simply find the value of x by doing this formula:

x+29°=90°

You then subtract 29° from both sides to simplify, and you come up with the solution

x=61°

Now we need to find the value of y.

To find the value of y I noticed that again, like x, y corresponds with another variable (being x) to form a perfect right angle (90°).

The way I realized this is a perfect right angle is because, as you can see in the picture you provided, the y+x angle are alternate exterior angles with another angle that is 90°.

Thus you can assume that:

x+y=90°

x= 61°

61°+y=90°

You then subtract 61° from both sides to get:

y=29°

Answer:

0.267

Step-by-step explanation:

the answer is 0.267

The table shows the results for spinning the spinner 80 times. The relative frequency for the event​ "spin a 3​" is 0.32.

Relative frequency is the ratio of the considered sub-group's count to the total count. (so its frequency of the considered subgroup relative to the total frequency).

In the problem given,

The table shows the results for spinning the spinner 80 times.

Number of Outcomes of "Spin a 3"=16

Total Number of Trials =50

Therefore,

The relative frequency for the event​ "spin a 3​" = 16/50

                                                                             = 0.32

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Answer:

Step-by-step explanation:

IF 17 is in base 10

THEN

17₁₀ = 1 x 10¹ + 7 x 10⁰

10001₂ = 1 x 2⁴ + 0 x 2³ + 0 x 2² + 0 x 2¹ + 1 x 2⁰

32₅ = 3 x 5¹ + 2 x 5⁰